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Lakshmi Kantha and Hubert Luce

Abstract

Turbulent mixing in the interior of the oceans is not as well understood as mixing in the oceanic boundary layers. Mixing in the generally stably stratified interior is primarily, although not exclusively, due to intermittent shear instabilities. Part of the energy extracted by the Reynolds stresses acting on the mean shear is expended in increasing the potential energy of the fluid column through a buoyancy flux, while most of it is dissipated. The mixing coefficient χ m, the ratio of the buoyancy flux to the dissipation rate of turbulence kinetic energy ε, is an important parameter, since knowledge of χ m enables turbulent diffusivities to be inferred. Theory indicates that χ m must be a function of the gradient Richardson number. Yet, oceanic studies suggest that a value of around 0.2 for χ m gives turbulent diffusivities that are in good agreement with those inferred from tracer studies. Studies by scientists working with atmospheric radars tend to reinforce these findings but are seldom referenced in oceanographic literature. The goal of this paper is to bring together oceanographic, atmospheric, and laboratory observations related to χ m and to report on the values deduced from in situ data collected in the lower troposphere by unmanned aerial vehicles, equipped with turbulence sensors and flown in the vicinity of the Middle and Upper Atmosphere (MU) radar in Japan. These observations are consistent with past studies in the oceans, in that a value of around 0.16 for χ m yields good agreement between ε derived from turbulent temperature fluctuations using this value and ε obtained directly from turbulence velocity fluctuations.

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Atsushi Kudo, Hubert Luce, Hiroyuki Hashiguchi, and Richard Wilson

Abstract

Deep turbulent layers can sometimes be observed on the underside of clouds that extend above upper-level frontal zones. In a recent study based on 3D numerical simulations with idealized initial conditions, it was found that midlevel cloud-base turbulence (MCT) can result from Rayleigh–Bénard-like convection as a result of cooling by sublimation of precipitating snow into dry and weakly stratified subcloud layers. In the present study, numerically simulated MCT was compared with a turbulent layer detected by the very high-frequency (VHF) middle- and upper-atmosphere (MU) radar during the passage of an upper-level front topped by clouds. The simulations were initialized with thermodynamic parameters derived from simultaneous radiosonde data. It was found that some important features of the simulated MCT (such as the scale of convection and vertical wind velocity perturbations) agreed quantitatively well with those reported in radar observations. Even if the possibility of other generation mechanisms cannot be ruled out, the good agreement strongly suggests that the MU radar actually detected MCT.

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Lydi Sma, Hubert Luce, Michel Crochet, and Shoichiro Fukao

Abstract

Frequency hopping [also recently called range imaging (RIM) or frequency domain interferometric imaging (FII)] is a pulse compression technique used to improve the range resolution Δr of Doppler radars limited by their minimum transmitted pulse length. This technique can be seen as an extension of the dual-frequency domain interferometry (FDI) technique, since it consists of transmitting more than two adjacent frequencies. Similarly to antenna array processing used for angular scanning, RIM/FII enables range scanning along the vertical line of sight to obtain a range profile (classically called “brightness” in the literature of the field of antenna array processing). The performances of RIM/FII can be improved by using high-resolution methods such as the maximum likelihood method (or the Capon method), the singular value decomposition method with the multiple signal classification (MUSIC) algorithm, and the newly introduced improved maximum likelihood method (the Lagunas–Gasull method). The applications of such methods would permit us to investigate in detail the small-scale dynamics within the stratified atmosphere where very thin structures, such as temperature sheets, coexist with thin turbulent layers. First, simulations are presented in order to compare the performances of the Lagunas–Gasull method with respect to the other methods already discussed by Palmer et al. and Luce et al. The second part of this paper is devoted to presenting some preliminary results with a 45-MHz miniradar profiler located at Toulon, France (43.7°N, 5.58°E), and to show other applications of the Lagunas–Gasull method on data collected with the VHF middle- and upper-atmosphere (MU) radar located at Shigaraki, Japan (34.85°N, 136.10°E). These results demonstrate the applicability of the Lagunas–Gasull method on two different VHF Doppler radars.

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Richard Wilson, Hubert Luce, Francis Dalaudier, and Jacques Lefrère

Abstract

The Thorpe analysis is a recognized method used to identify and characterize turbulent regions within stably stratified fluids. By comparing an observed profile of potential temperature or potential density to a reference profile obtained by sorting the data, overturns resulting in statically unstable regions, mainly because of turbulent patches and Kelvin–Helmholtz billows, can be identified. However, measurement noise may induce artificial inversions of potential temperature or density, which can be very difficult to distinguish from real (physical) overturns.

A method for selecting real overturns is proposed. The method is based on the data range statistics; the range is defined as the difference between the maximum and the minimum of the values in a sample. A statistical hypothesis test on the range is derived and evaluated through Monte Carlo simulations. Basically, the test relies on a comparison of the range of a data sample with the range of a normally distributed population of the same size as the data sample. The power of the test, that is, the probability of detecting the existing overturns, is found to be an increasing function of both trend-to-noise ratio (tnr) and overturns size. A threshold for the detectable size of the overturns as a function of tnr is derived. For very low tnr data, the test is shown to be unreliable whatever the size of the overturns. In such a case, a procedure aimed to increase the tnr, mainly based on subsampling, is described.

The selection procedure is applied to atmospheric data collected during a balloon flight with low and high vertical resolutions. The fraction of the vertical profile selected as being unstable (turbulent) is 47% (27%) from the high (low) resolution dataset. Furthermore, relatively small tnr measurements are found to give rise to a poor estimation of the vertical extent of the overturns.

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Hubert Luce, Takuji Nakamura, Masayuki K. Yamamoto, Mamoru Yamamoto, and Shoichiro Fukao

Abstract

Turbulence generation mechanisms prevalent in the atmosphere are mainly shear instabilities, breaking of internal buoyancy waves, and convective instabilities such as thermal convection due to heating of the ground. In the present work, clear-air turbulence underneath a cirrus cloud base is described owing to coincident observations from the VHF (46.5 MHz) middle and upper atmosphere (MU) radar, a Rayleigh–Mie–Raman (RMR) lidar, and a balloon radiosonde on 7–8 June 2006 (at Shigaraki, Japan; 34.85°N, 136.10°E). Time–height cross section of lidar backscatter ratio obtained at 2206 LT 7 June 2006 showed the presence of a cirrus layer between 8.0 and 12.5 km MSL. Downward-penetrating structures of ice crystals with horizontal and vertical extents of 1.0–4.0 km and 200–800 m, respectively, have been detected at the cirrus cloud base for about 35 min. At the same time, the MU radar data revealed clear-air turbulence layers developing downward from the cloud base in the environment of the protuberances detected by the RMR lidar. Their maximum depth was about 2.0 km for about 1.5 h. They were associated with oscillatory vertical wind perturbations of up to ±1.5 m s−1 and variances of Doppler spectrum of 0.2–1.5 m−2 s−2. Analysis of the data suggests that the turbulence and the downward penetration of cloudy air were possibly the consequence of a convective instability (rather than a dynamical shear instability) that was likely due to sublimation of ice crystals in the subcloud region. Downward clear-air motions measured by the MU radar were associated with the descending protuberances, and updrafts were observed between them. These observations suggest that the cloudy air might have been pushed down by the downdrafts of the convective instability and pushed up by the updrafts to form the observed protuberances at the cloud base. These structures may be virga or perhaps more likely mamma as reported by recent observations of cirrus mamma with similar instruments and by numerical simulations.

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Hubert Luce, Lakshmi Kantha, Hiroyuki Hashiguchi, Abhiram Doddi, Dale Lawrence, and Masanori Yabuki

Abstract

Under stably stratified conditions, the dissipation rate ε of turbulence kinetic energy (TKE) is related to the structure function parameter for temperature CT2, through the buoyancy frequency and the so-called mixing efficiency. A similar relationship does not exist for convective turbulence. In this paper, we propose an analytical expression relating ε and CT2 in the convective boundary layer (CBL), by taking into account the effects of nonlocal heat transport under convective conditions using the Deardorff countergradient model. Measurements using unmanned aerial vehicles (UAVs) equipped with high-frequency response sensors to measure velocity and temperature fluctuations obtained during the two field campaigns conducted at Shigaraki MU observatory in June 2016 and 2017 are used to test this relationship between ε and CT2 in the CBL. The selection of CBL cases for analysis was aided by auxiliary measurements from additional sensors (mainly radars), and these are described. Comparison with earlier results in the literature suggests that the proposed relationship works, if the countergradient term γ D in the Deardorff model, which is proportional to the ratio of the variances of potential temperature θ and vertical velocity w, is evaluated from in situ (airplane and UAV) observational data, but fails if evaluated from large-eddy simulation (LES) results. This appears to be caused by the tendency of the variance of θ in the upper part of the CBL and at the bottom of the entrainment zone to be underestimated by LES relative to in situ measurements from UAVs and aircraft. We discuss this anomaly and explore reasons for it.

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